Computer algebra systems are gaining more and more importance in all areas
of science and engineering. This textbook gives a thorough introduction to
the algorithmic basis of the mathematical engine in computer
algebra systems.

It is designed to accompany one- or two-semester courses for advanced
undergraduate or graduate students in computer science or mathematics.
Its comprehensiveness and authority make it also an
essential reference for professionals in the area.

Special features include: detailed study of algorithms including time
analysis; implementation reports on several topics; complete proofs of the
mathematical underpinnings; a wide variety of applications (among others, in
chemistry, coding theory, cryptography, computational logic, and the design
of calendars and musical scales). Some of this material has never appeared
before in book form. Finally, a great deal of historical information and
illustration
enlivens the text.